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 A343424 Numbers k such that sopfr((k-1)!) is divisible by k, where sopfr(k) = A001414(k) = sum of primes, with repetition, dividing k. 1
 1, 2, 45, 53, 177, 436, 1239, 3651, 6463, 6869, 10753, 19450, 29721, 33289, 88907, 93682, 1137232, 1516121, 4361271, 9428534, 43778664, 74738670, 271442366, 775223371, 835126289, 1736463189, 3088442241, 5054888590, 11184483614, 16993011938, 30788570768, 33342871740 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A025281(k-1) for the values of sopfr((k-1)!). LINKS Martin Ehrenstein, Table of n, a(n) for n = 1..35 EXAMPLE 45 is a term as sopfr(44!) = 585 which is divisible by 45. MATHEMATICA sopfr[0] = sopfr[1] = 0; sopfr[n_] := Plus @@ Times @@@ FactorInteger[n]; sum = 0; s = {}; Do[sum += sopfr[n]; If[Divisible[sum, n + 1], AppendTo[s, n + 1]], {n, 0, 10^6}]; s (* Amiram Eldar, May 06 2021 *) PROG (PARI) sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414 isok(k) = !(sopfr((k-1)!) % k); \\ Michel Marcus, May 06 2021 CROSSREFS Cf. A001414, A025281, A027746. Sequence in context: A342827 A264438 A241762 * A041241 A304015 A279680 Adjacent sequences:  A343421 A343422 A343423 * A343425 A343426 A343427 KEYWORD nonn AUTHOR Scott R. Shannon, Apr 15 2021 EXTENSIONS a(27) from Amiram Eldar, May 06 2021 a(28) and beyond from Martin Ehrenstein, May 16 2021 STATUS approved

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Last modified August 9 15:30 EDT 2022. Contains 356026 sequences. (Running on oeis4.)